Vibratory sensor and method of varying vibration in a vibratory sensor

ABSTRACT

A vibratory sensor ( 5 ) includes a vibratory element ( 104 ), a receiver circuit ( 134 ) that receives a vibration signal from the vibratory element ( 104 ), and a drive circuit ( 138 ) that generates a drive signal. The drive circuit ( 138 ) includes a closed-loop drive ( 143 ) and an open-loop drive ( 147 ). The meter electronics ( 20 ) vibrates the vibratory element ( 104 ) commencing at a commanded first frequency and in an open-loop manner to achieve a first target phase difference ϕ1 for a fluid being characterized and determines a corresponding first frequency point ω1, vibrates the vibratory element ( 104 ) commencing at a commanded second frequency and in the open-loop manner to achieve a second target phase difference ϕ2 and determines a corresponding second frequency point ω2, and determines a viscosity of the fluid being characterized using the first frequency point ω1 and the second frequency point ω2.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a Divisional Application of and claims the benefit of U.S.application Ser. No. 14/782,135, with a filing date of Oct. 2, 2015,entitled “VIBRATORY SENSOR AND METHOD OF VARYING VIBRATION IN AVIBRATORY SENSOR,” which is a National Stage entry of InternationalApplication No. PCT/US2013/043568, with an international filing date ofMay 31, 2013, entitled “VIBRATORY SENSOR AND METHOD OF VARYING VIBRATIONIN A VIBRATORY SENSOR,” which claims the benefit of ProvisionalApplication No. 61/816,221, filed Apr. 26, 2013, entitled “VIBRATORYSENSOR AND METHOD OF VARYING VIBRATION IN A VIBRATORY SENSOR.”

BACKGROUND OF THE INVENTION 1. Field of the Invention

The present invention relates to a vibratory sensor and method ofvarying vibration in a vibratory sensor.

2. Statement of the Problem

Vibratory sensors, such as vibratory densitometers and vibratoryviscometers, operate by detecting motion of a vibrating element thatvibrates in the presence of a fluid to be characterized. Propertiesassociated with the fluid, such as density, viscosity, temperature andthe like, can be determined by processing a vibration signal or signalsreceived from one or more motion transducers associated with thevibrating element. The vibration of the vibrating element is generallyaffected by the combined mass, stiffness and damping characteristics ofthe vibrating element in combination with the fluid.

The viscosity of a fluid can be measured by generating vibrationresponses at frequencies ω1 and ω2 that are above and below a resonantfrequency ω0 of the combined fluid and vibratory sensor. At theresonance frequency ω0, the phase difference ϕ0 may be about 90 degrees.The two frequency points ω1 and ω2 are defined as the drive frequencieswhere the drive signal phase and the vibration signal phase differ bythe phase differences ϕ1 and ϕ2, respectively. The phase difference ϕ1may be defined as the point where the phase difference between the drivesignal phase and the vibration signal phase is about 135 degrees. Thephase difference ϕ2 may be defined as the point where the phasedifference between the drive signal phase and the vibration signal phaseis about 45 degrees.

The distance between these two frequency points ω1 and ω2 (i.e., thedifference in frequency between ω1 and ω2) is used to determine the termQ, which is proportional to viscosity and can be approximated by theformula:

viscosity Q=ω0/(ω2−ω1)   (1)

The resonant frequency ω0 is centered between the two frequency pointsω1 and ω2. Therefore, the resonant frequency ω0 can be defined as:

ω0≈0.5* (ω2+ω1)   (2)

The frequency points ω1 and ω2 are determined during operation when thesensor element interacts with the fluid to be characterized. In order toproperly determine the frequency points ω1 and ω2, the prior art drivesystem uses a closed loop drive, driving the sensor element to alternatebetween the two phase difference points (ϕ1 and ϕ2) and recording thevibration frequencies ω1 and ω2 at these points. By using a closed-loopdrive, the prior art drive system ensures that the phase differencemeasurement is stable when the vibration frequencies ω1 and ω2 aredetermined.

Alternatively, the frequency points ω1 and ω2 are defined as half-powerpoints, as they comprise frequency points where the power in thevibration signal has half the power of the resonant frequency ω0, orwhere the half-power point amplitude A_(half) is (A_(half)=A₀/√2). TheA₀ term is the amplitude of the vibration signal at the resonantfrequency ω0. The two frequency points ω1 and ω2 are also known as 3 dBpoints, where the vibration signal power is 3 dB down from the resonantfrequency power.

FIG. 1 shows a prior art vibratory sensor comprising a vibratory sensorelement and a signal processor coupled to the sensor element. The priorart vibratory sensor includes a driver for vibrating a sensor elementand a pickoff sensor that creates a vibration signal in response to thevibration. The vibration signal is sinusoidal in nature. The signalprocessor receives the vibration signal and processes the vibrationsignal to generate one or more fluid characteristics or fluidmeasurements. The signal processor determines both the frequency and theamplitude of the vibration signal. The frequency and amplitude of thevibration signal can be further processed to determine a density of thefluid, or can be processed to determined additional or other fluidcharacteristics, such as the viscosity.

The prior art signal processor generates a drive signal for the driverusing a closed-loop drive circuit. The drive signal typically is basedon the received vibration signal, wherein the prior art closed-loopdrive circuit processes the received vibration signal to create thedrive signal. The drive signal may be based on the frequency andamplitude of the received vibration signal, wherein the receivedvibration signal comprises feedback that enables the prior art drivesystem to achieve a target vibration. The prior art vibratory sensordrives the sensor element using the closed-loop drive and using afeedback element, wherein the closed-loop drive incrementally changesthe drive frequency and monitors the feedback element until the desiredtarget point is reached. The desired endpoint comprises a phasedifference (ϕ) between the drive signal and the resulting pickoff signalachieving the phase difference ϕ1 or the phase difference ϕ2.

FIG. 2 is a flow chart of a method of operation of the prior artvibratory sensor for measuring fluid viscosity. Steps 1-4 belowdetermine the frequency of the first frequency point ω1 while steps 5-8determine the frequency of the second frequency point ω2.

In step 1, a vibration setpoint is set to a first target phasedifference ϕ1 and the sensor element is vibrated from the currentvibration frequency. The first target phase difference ϕ1 is achieved byvarying the frequency of the drive signal, starting from the currentvibration frequency. The current vibration frequency is graduallychanged in a closed-loop manner and according to received feedback, suchas feedback regarding the difference between a current phase differenceand the target phase difference. The vibration frequency isincrementally ramped up or down from the current vibration frequency,depending on whether the phase difference is to be increased ordecreased.

In step 2, the current phase difference is compared to the first targetphase difference ϕ1. If the first target phase difference ϕ1 has beenachieved, then the method proceeds to step 4. Otherwise, the methodbranches to step 3 until the first target phase difference ϕ1 isachieved.

In step 3, a wait is performed. Consequently, the method loops and waitsuntil the vibration setpoint has been achieved. The prior art vibratorysensor therefore waits for the actual vibration of the sensor element toreach the vibration setpoint. Due to the closedloop drive operation, thesensor element does not achieve vibration at the vibration setpointuntil at least a known wait time has elapsed.

The wait may be for a fixed predetermined time or may vary in length.Environmental conditions may require a longer than expected time toachieve the target phase difference. The length of the wait may dependon various factors. The length of the wait may depend on a distance tothe target phase difference from the initial phase difference. Thelength of the wait may depend on the physical characteristics of thesensor element. The length of the wait may depend on the nature of thefluid being measured (including the density and/or viscosity of thefluid). The length of the wait may depend on the power available to theprior art vibratory sensor.

In step 4, where the vibration setpoint has been achieved and the phasedifference between the drive sensor signal and the pickoff sensor signalcorresponds to the first phase difference ϕ1, then the correspondingfirst vibration frequency ω1 is recorded.

The first frequency point ω1 comprises the vibration frequency thatgenerates the first target phase difference ϕ1. The first vibrationfrequency ω1 may comprise the frequency where the phase differencebetween the drive signal phase and the pickoff signal phase is about 135degrees, for example.

In step 5, the vibration setpoint is set to a second target phasedifference ϕ2 and the sensor element is vibrated from the currentvibration frequency. The second target phase difference ϕ2 is achievedby varying the frequency of the drive signal, starting from the currentvibration frequency. The current vibration frequency is graduallychanged in a closed-loop manner and according to received feedback, suchas feedback regarding the difference between a current phase differenceand the target phase difference. The vibration frequency isincrementally ramped up or down from the current vibration frequency,depending on whether the phase difference is to be increased ordecreased. It should be understood that the starting vibration frequencyis therefore the current vibration frequency, which comprises thevibration frequency obtained in step 4 above.

In step 6, the current phase difference is compared to the second targetphase difference ϕ2. If the second target phase difference ϕ2 has beenachieved, then the method proceeds to step 8. Otherwise, the methodbranches to step 7 until the second target phase difference ϕ2 isachieved.

In step 7, a wait is performed. Consequently, the method loops and waitsuntil the vibration setpoint has been achieved. Due to the closedloopdrive operation, the sensor element does not achieve vibration at thevibration setpoint until at least a known wait time has elapsed, aspreviously discussed.

In step 8, where the vibration setpoint has been achieved and the phasedifference between the drive sensor signal and the pickoff sensor signalcorresponds to the second phase difference ϕ2, then the correspondingsecond frequency point ω2 is recorded. The second frequency point ω2comprises the vibration frequency that generates the second target phasedifference ϕ2. The second frequency point ω2 may comprise the frequencywhere the phase difference between the drive signal phase and thepickoff signal phase is about 45 degrees, for example.

FIG. 3 is a graph of a closed-loop vibration response of the prior artvibratory sensor of FIG. 1. The vertical axis represents vibrationfrequency (ω) and the horizontal axis represents time (t). It can beseen that the prior art vibratory sensor is alternatingly vibrated atthe first frequency point ω1 and then at the second frequency point ω2,wherein this pattern is iteratively repeated. It should be understoodthat the first and second frequency points ω1 and ω2 are not necessarilyconstant. The first and second vibration frequencies ω1 and ω2 maychange due to changes in the fluid being characterized by the vibratorysensor, for example.

Due to the closed-loop design of the drive portion of the prior artvibratory sensor, it can be seen that the actual vibration frequencychanges smoothly and continuously, but slowly. Each change in drivefrequency requires a closed-loop time period T_(CL) to accomplish, dueto the feedback used to achieve the target phase difference. As aresult, the prior art vibratory tine sensor cannot measure rapid changesin ω1 and ω2, and therefore cannot measure rapid changes in viscosity ofthe fluid to be characterized. Further, even where the time periodT_(CL) is small, it can be seen that the time period T_(CL) is repeatedand will therefore add up and will affect the operation of the prior artvibratory sensor.

Aspects of the Invention

In one aspect of the invention, a vibratory sensor comprises:

-   -   a vibratory element configured to generate a vibration signal;        and    -   a receiver circuit that receives the vibration signal from the        vibratory element; and    -   a drive circuit coupled to the receiver circuit and the        vibratory element and generating a drive signal that vibrates        the vibratory element, wherein the drive circuit vibrates the        vibratory element commencing at a commanded first frequency and        in an open-loop manner to achieve a first target phase        difference ϕ1 for a fluid being characterized and determines a        corresponding first frequency point ω1, vibrates the vibratory        element commencing at a commanded second frequency and in the        open-loop manner to achieve a second target phase difference ϕ2        and determines a corresponding second frequency point ω2, and        determines a viscosity of the fluid being characterized using        the first frequency point ω1 and the second frequency point ω2.

Preferably, the vibratory sensor iteratively performs the vibrating anddetermining steps.

Preferably, the commanded first frequency comprises a previous-timefirst frequency point ω1 _(time=(t-1)) and the commanded secondfrequency comprises a previous-time second frequency point ω2_(time=(t-1)).

Preferably, the drive circuit comprises a closed-loop drive thatgenerates the drive signal to achieve a target phase difference andcommencing at a current vibration frequency and an open-loop drive thatgenerates the drive signal to achieve a target phase difference andcommencing at a commanded first or second frequency.

Preferably, vibrating the vibratory element of the vibratory sensor inthe open-loop manner comprises the drive circuit setting a vibrationsetpoint to the first target phase difference ϕ1, the drive circuitvibrating the vibratory element in the open-loop manner and at thecommanded first frequency, the drive circuit comparing a current firstphase difference to the first target phase difference ϕ1 and waitinguntil the current first phase difference is substantially equal to thefirst target phase difference ϕ1, if the current first phase differenceis equal to the first target phase difference ϕ1, then the drive circuitrecording the corresponding first frequency point ω1, wherein achievingthe first target phase difference ϕ1 generates the first frequency pointω1 in the vibratory element, the drive circuit setting the vibrationsetpoint to the second target phase difference ϕ2, the drive circuitvibrating the vibratory element in the open-loop manner and at thecommanded second frequency, the drive circuit comparing a current secondphase difference to the second target phase difference ϕ2 and waitinguntil the current second phase difference is substantially equal to thesecond target phase difference ϕ2, and if the current second phasedifference is equal to the second target phase difference ϕ2, then thedrive circuit recording the corresponding second frequency point ω2,wherein achieving the second target phase difference ϕ2 generates thesecond frequency point ω2 in the vibratory element.

Preferably, the drive circuit is further configured to vibrate thevibratory element in a closed-loop manner to achieve the first targetphase difference ϕ1 for the fluid being characterized and determining acorresponding first frequency point ω1, with the vibrating commencing atthe current vibration frequency, and vibrate the vibratory element inthe closed-loop manner to achieve the second target phase difference ϕ2for the fluid being characterized and determining a corresponding secondfrequency point ω2, with the vibrating commencing at the currentvibration frequency.

Preferably, the drive circuit selects the open-loop operation if thefluid being characterized is substantially stable.

Preferably, the drive circuit is further configured to vibrate thevibratory element commencing at the commanded first frequency and in theopen-loop manner to approximate the first target phase difference ϕ1 fora fluid being characterized, vibrate the vibratory element in aclosed-loop manner to achieve the first target phase difference ϕ1 anddetermine a corresponding first frequency point ω1, vibrate thevibratory element commencing at the commanded second frequency and inthe open-loop manner to approximate the second target phase differenceϕ2 for the fluid being characterized, vibrate the vibratory element inthe closed-loop manner to achieve the second target phase difference ϕ2and determine a corresponding second frequency point ω2, and determine aviscosity of the fluid being characterized using the first frequencypoint ω1 and the second frequency point ω2.

Preferably, the receiver circuit is coupled to the drive circuit, withthe receiver circuit providing the vibration signal amplitude and thevibration signal frequency to the drive circuit, with the drive circuitgenerating a drive signal for the vibratory element using the vibrationsignal amplitude and the vibration signal frequency.

Preferably, the vibratory sensor comprises a vibratory tine sensor andwith the vibratory element comprising a tuning fork structure.

In one aspect of the invention, a method of varying vibration in avibratory sensor comprises:

-   -   vibrating a vibratory element of a vibratory sensor commencing        at a commanded first frequency and in an open-loop manner to        achieve a first target phase difference ϕ1 for a fluid being        characterized and determining a corresponding first frequency        point ω1;    -   vibrating the vibratory element commencing at a commanded second        frequency and in the open-loop manner to achieve a second target        phase difference ϕ2 and determining a corresponding second        frequency point ω2; and    -   determining a viscosity of the fluid being characterized using        the first frequency point ω1 and the second frequency point ω2.

Preferably, the method iteratively performs the vibrating anddetermining steps.

Preferably, the commanded first frequency comprises a previous-timefirst frequency point ω1 _(time=(t-1)) and the commanded secondfrequency comprises a previous-time second frequency point ω2_(time=(t-1)).

Preferably, vibrating the vibratory element in the open-loop mannercomprises setting a vibration setpoint to the first target phasedifference ϕ1, vibrating the vibratory element in the open-loop mannerand at the commanded first frequency, comparing a current first phasedifference to the first target phase difference ϕ1 and waiting until thecurrent first phase difference is substantially equal to the firsttarget phase difference ϕ1, if the current first phase difference isequal to the first target phase difference ϕ1, then recording thecorresponding first frequency point ω1, wherein achieving the firsttarget phase difference ϕ1 generates the first frequency point ω1 in thevibratory element, setting the vibration setpoint to the second targetphase difference ϕ2, vibrating the vibratory element in the open-loopmanner and at the commanded second frequency, comparing a current secondphase difference to the second target phase difference ϕ2 and waitinguntil the current second phase difference is substantially equal to thesecond target phase difference ϕ2, and if the current second phasedifference is equal to the second target phase difference ϕ2, thenrecording the corresponding second frequency point ω2, wherein achievingthe second target phase difference ϕ2 generates the second frequencypoint ω2 in the vibratory element.

Preferably, the method further comprises the preliminary steps ofvibrating the vibratory element in a closed-loop manner to achieve thefirst target phase difference ϕ1 for the fluid being characterized anddetermining a corresponding first frequency point ω1, with the vibratingcommencing at the current vibration frequency, and vibrating thevibratory element in the closed-loop manner to achieve the second targetphase difference ϕ2 for the fluid being characterized and determining acorresponding second frequency point ω2, with the vibrating commencingat the current vibration frequency.

Preferably, the method selects the open-loop operation if the fluidbeing characterized is substantially stable.

Preferably, the method comprises vibrating the vibratory elementcommencing at the commanded first frequency and in the open-loop mannerto approximate the first target phase difference ϕ1 for a fluid beingcharacterized, vibrating the vibratory element in a closed-loop mannerto achieve the first target phase difference ϕ1 and determining acorresponding first frequency point ω1, vibrating the vibratory elementcommencing at the commanded second frequency and in the open-loop mannerto approximate the second target phase difference ϕ2 for the fluid beingcharacterized, vibrating the vibratory element in the closed-loop mannerto achieve the second target phase difference ϕ2 and determining acorresponding second frequency point ω2, and determining a viscosity ofthe fluid being characterized using the first frequency point ω1 and thesecond frequency point ω2.

Preferably, the vibratory sensor comprises a vibratory tine sensor andwith the vibratory element comprising a tuning fork structure.

DESCRIPTION OF THE DRAWINGS

The same reference number represents the same element on all drawings.The drawings are not necessarily to scale.

FIG. 1 shows a prior art vibratory sensor comprising a vibratory sensorelement and a signal processor coupled to the sensor element comprisinga vibratory sensor element and a signal processor coupled to the sensorelement.

FIG. 2 is a flow chart of a method of operation of the prior artvibratory sensor for measuring fluid viscosity.

FIG. 3 is a graph of a closed-loop vibration response of the prior artvibratory sensor of FIG. 1.

FIG. 4 shows a vibratory sensor according to an embodiment of theinvention.

FIG. 5 shows the vibratory sensor according to an embodiment of theinvention.

FIG. 6 is a flowchart of a method of varying vibration in the vibratorysensor according to an embodiment of the invention.

FIG. 7 is a graph of the combined closed-loop and open-loop vibrationresponse of the vibratory sensor.

DETAILED DESCRIPTION OF THE INVENTION

FIGS. 4-7 and the following description depict specific examples toteach those skilled in the art how to make and use the best mode of theinvention. For the purpose of teaching inventive principles, someconventional aspects have been simplified or omitted. Those skilled inthe art will appreciate variations from these examples that fall withinthe scope of the invention. Those skilled in the art will appreciatethat the features described below can be combined in various ways toform multiple variations of the invention. As a result, the invention isnot limited to the specific examples described below, but only by theclaims and their equivalents.

FIG. 4 shows a vibratory sensor 5 according to an embodiment of theinvention. The vibratory sensor 5 may comprise a vibratory element 104and meter electronics 20, wherein the vibratory element 104 is coupledto the meter electronics 20 by a lead or leads 100. In some embodiments,the vibratory sensor 5 may comprise a vibratory tine sensor or forkdensity sensor (see FIG. 5 and the accompanying discussion). However,other vibratory sensors are contemplated and are within the scope of thedescription and claims.

The vibratory sensor 5 may be at least partially immersed into a fluidto be characterized. For example, the vibratory sensor 5 may be mountedin a pipe or conduit. The vibratory sensor 5 may be mounted in a tank orcontainer or structure for holding a fluid. The vibratory sensor 5 maybe mounted in a manifold or similar structure for directing a fluidflow. Other mounting arrangements are contemplated, however, and arewithin the scope of the description and claims.

The fluid can comprise a liquid. The fluid can comprise a gas.Alternatively, the fluid can comprise a multi-phase fluid, such as aliquid that includes entrained gas, entrained solids, multiple liquids,or combinations thereof.

The vibratory sensor 5 may operate to provide fluid measurements. Thevibratory sensor 5 may provide fluid measurements including one or moreof a fluid density and a fluid viscosity for a fluid, including flowingor non-flowing fluids. The vibratory sensor 5 may provide fluidmeasurements including a fluid mass flow rate, a fluid volume flow rate,and/or a fluid temperature. This listing is not exhaustive and thevibratory sensor 5 may measure or determine other fluid characteristics.

The meter electronics 20 may provide electrical power to the vibratoryelement 104 via the lead or leads 100. The meter electronics 20 maycontrol operation of the vibratory element 104 via the lead or leads100. For example, the meter electronics 20 may generate a drive signaland supply the drive signal to the vibratory element 104, wherein thevibratory element 104 generates a vibration in one or more vibratorycomponents using the drive signal. The drive signal may control thevibrational amplitude. The drive signal may control the vibrationalfrequency. The drive signal may control the vibrational duration and/orvibrational timing.

The meter electronics 20 may receive a vibration signal or signals fromthe vibratory element 104 via the lead or leads 100. The meterelectronics 20 may process the vibration signal or signals in order togenerate a density measurement, for example. It should be understoodthat other or additional measurements may be generated from thevibration signal or signals.

The meter electronics 20 may process the vibration signal or signalsreceived from the vibratory element 104 to determine a frequency of thesignal or signals. The frequency may comprise a resonant frequency ofthe fluid. The resonant frequency may be used to determine a density ofthe fluid. Further, or in addition, the meter electronics may processthe vibration signal or signals to determine other characteristics ofthe fluid, such as a viscosity or a phase shift between signals that canbe processed to determine a fluid flow rate, for example. Othervibrational response characteristics and/or fluid measurements arecontemplated and are within the scope of the description and claims.

The meter electronics 20 may be further coupled to a communication link26. The meter electronics 20 may communicate a vibration signal over thecommunication link 26. The meter electronics 20 may process the receivedvibration signal to generate a measurement value or values and maycommunicate a measurement value or values over the communication link26.

In addition, the meter electronics 20 may receive information over thecommunication link 26. The meter electronics 20 may receive commands,updates, operational values or operational value changes, and/orprogramming updates or changes over the communication link 26.

FIG. 5 shows the vibratory sensor 5 according to an embodiment of theinvention. The vibratory sensor 5 in the embodiment shown comprises avibratory tine sensor 5, including meter electronics 20 coupled to thevibratory element 104 by a shaft 115 in the embodiment shown. The shaft115 may be of any desired length. The shaft 115 may be at leastpartially hollow and wires or other conductors may extend between themeter electronics 20 and the vibratory element 104 through the shaft115.

The meter electronics 20 may include circuit components such as areceiver circuit 134, a drive circuit 138, and an interface circuit 136in the embodiment shown.

In the embodiment shown, the receiver circuit 134 and the drive circuit138 are directly coupled to the leads of the vibratory element 104 inthe embodiment shown. Alternatively, the meter electronics 20 maycomprise a separate component or device from the vibratory element 104,wherein the receiver circuit 134 and the drive circuit 138 are coupledto the vibratory element 104 via the lead or leads 100, as shown in FIG.4.

The vibratory element 104 of the vibratory sensor 5 in the embodimentshown comprises a tuning fork structure 104, wherein the vibratoryelement 104 is at least partially immersed in the fluid being measured.The vibratory element 104 includes a housing 105 that may be affixed toanother structure, such as a pipe, conduit, tank, receptacle, manifold,or any other fluid-handling structure. The housing 105 retains thevibratory element 104, while the vibratory element 104 remains at leastpartially exposed. The vibratory element 104 therefore is configured tobe immersed in the fluid.

The vibratory element 104 in the embodiment shown includes first andsecond tines 112 and 114 that are configured to extend at leastpartially into the fluid. The first and second tines 112 and 114comprise elongate elements that may have any desired cross-sectionalshape. The first and second tines 112 and 114 may be at least partiallyflexible or resilient in nature.

The vibratory sensor 5 further includes corresponding first and secondpiezo elements 122 and 124 that comprise piezo-electric crystalelements. The first and second piezo elements 122 and 124 are locatedadjacent to the first and second tines 112 and 114, respectively. Thefirst and second piezo elements 122 and 124 are configured to contactand mechanically interact with the first and second tines 112 and 114.

The first piezo element 122 may contact at least a portion of the firsttine 112. The first piezo element 122 may be electrically coupled to thedrive circuit 138, with the drive circuit 138 providing a time-varyingdrive signal to the first piezo element 122. The first piezo element 122may expand and contract when subjected to the time-varying drive signal.As a result, the first piezo element 122 may alternatingly deform anddisplace the first tine 112 from side to side in a vibratory motion (seedashed lines), disturbing the fluid in a periodic, reciprocating manner.

The second piezo element 124 may be coupled to a receiver circuit 134that produces a time-varying vibration response signal corresponding tothe deformations of the second tine 114 in the fluid. Movement of thesecond tine 114 may therefore cause a corresponding electrical vibrationsignal to be generated by the second piezo element 124. The second piezoelement 124 transmits the vibration signal to the meter electronics 20.The meter electronics 20 processes the vibration signal and may measurethe vibration signal amplitude and/or the vibration signal frequency ofthe vibration signal.

The meter electronics 20 may include the interface circuit 136. Theinterface circuit 136 may be configured to communicate with externaldevices. The interface circuit 136 may communicate a vibrationmeasurement signal or signals and may communicate determined fluidcharacteristics to one or more external devices. The meter electronics20 may transmit vibration signal characteristics via the interfacecircuit 136, such as a vibration signal frequency and/or a vibrationsignal amplitude of the vibration signal. The meter electronics 20 maytransmit fluid measurements via the interface circuit 136, such as adensity and/or viscosity of the fluid, among other things. Other fluidmeasurements are contemplated and are within the scope of thedescription and claims. In addition, the interface circuit 136 mayreceive communications from external devices, including commands anddata for generating measurement values, for example.

In some embodiments, the receiver circuit 134 is coupled to the drivecircuit 138, with the receiver circuit 134 providing the vibrationsignal amplitude and the vibration signal frequency to the drive circuit138, with the drive circuit 138 generating a drive signal for thevibratory element 104 using the vibration signal amplitude and thevibration signal frequency.

The drive circuit 138 may receive the vibration signal and may generatea drive signal from the vibration signal, and may modify characteristicsof the vibration signal in order to generate the drive signal. Thevibratory element 104 is generally maintained at a resonant frequency,as influenced by the surrounding fluid. The vibratory element 104 istypically maintained at the resonant frequency by the drive circuit 138.The drive circuit 138 may modify the vibration signal to produce adesired vibrational disturbance in the fluid. The drive circuit 138further may modify the vibration signal to compensate for the length ofthe leads between the meter electronics 20 and the vibratory element 104and/or to compensate for other losses in the vibration signal, forexample.

The drive circuit 138 may include a closed-loop drive 143 and anopen-loop drive 147. Either one of the closed-loop drive 143 or theopen-loop drive 147 may be used by the drive circuit 138 to generate adrive signal and supply the drive signal to the vibratory element 104(i.e., to the first piezo element 122).

The closed-loop drive 143 generates a closed-loop drive signal, whereinthe closed-loop drive 143 uses the vibration signal received from thevibratory element 104 (i.e., from the second piezo element 124) togenerate the drive signal. The closed-loop drive 143 therefore operatesbased on feedback and a feedback algorithm. The feedback comprises adifference between the current vibration and the commanded vibrationtarget. The drive signal is smoothly and continuously varied by theclosed-loop drive 143 until the vibration signal (i.e., the feedback)reaches the vibration target. Therefore, if a first frequency point ω1is commanded, the closed-loop drive 143 will incrementally change from acurrent vibration frequency of ω2 until the target vibration of ω1 iseventually achieved.

In some embodiments, the drive circuit 138 comprises a closed-loop drive143 that generates the drive signal to achieve a target phasedifference, commencing at a current vibration frequency, and anopen-loop drive 147 that generates the drive signal to achieve a targetphase difference, commencing at a commanded vibration frequency.

The open-loop drive 147 is configured to generate a drive signal basedon a commanded vibration target. Therefore, if a first vibrationfrequency is commanded, the open-loop drive 147 will generate a drivesignal at the first vibration frequency, even where the drive circuit138 had been vibrating the vibratory element 104 at the second vibrationfrequency. The open-loop drive 147 does not operate based on feedbackand the open-loop drive 147 therefore can immediately vibrate at acommanded vibration target.

In some embodiments, the drive circuit 138 vibrates the vibratoryelement 104 commencing at a commanded first frequency and in anopen-loop manner to achieve a first target phase difference ϕ1 for afluid being characterized and determines a corresponding first frequencypoint ω1, vibrates the vibratory element 104 commencing at a commandedsecond frequency and in the open-loop manner to achieve a second targetphase difference ϕ2 and determines a corresponding second frequencypoint ω2, and determines a viscosity of the fluid being characterizedusing the first frequency point ω1 and the second frequency point ω2.

It should be understood that the commanded first and second frequenciesare only approximations of the first and second frequency points ω1 andω2. The commanded first and second frequencies may not be exactly thefinal values of the actual first and second frequency points ω1 and ω2,such as where the density of the fluid is varying over time.

In some embodiments, vibrating the vibratory element 104 of thevibratory sensor 5 in the open-loop manner comprises the drive circuit138 setting a vibration setpoint to the first target phase differenceϕ1, the drive circuit 138 vibrating the vibratory element 104 commencingat the commanded first frequency and in the open-loop manner, the drivecircuit 138 comparing a current first phase difference to the firsttarget phase difference ϕ1 and waiting until the current first phasedifference is substantially equal to the first target phase differenceϕ1, if the current first phase difference is equal to the first targetphase difference ϕ1, then the drive circuit 138 recording thecorresponding first frequency point ω1, wherein achieving the firsttarget phase difference ϕ1 generates the first frequency point ω1 in thevibratory element 104, the drive circuit 138 setting the vibrationsetpoint to the second target phase difference ϕ2, the drive circuit 138vibrating the vibratory element 104 commencing at the commanded secondfrequency and in the open-loop manner, the drive circuit 138 comparing acurrent second phase difference to the second target phase difference ϕ2and waiting until the current second phase difference is substantiallyequal to the second target phase difference ϕ2, and if the currentsecond phase difference is equal to the second target phase differenceϕ2, then the drive circuit 138 recording the corresponding secondfrequency point ω2, wherein achieving the second target phase differenceϕ2 generates the second frequency point ω2 in the vibratory element 104.

In some embodiments, the drive circuit 138 is configured to vibrate thevibratory element 104 commencing at a commanded first frequency and inthe open-loop manner to approximate a first target phase difference ϕ1for a fluid being characterized, vibrate the vibratory element 104 in aclosed-loop manner to achieve the first target phase difference ϕ1 anddetermining a corresponding first frequency point ω1, vibrate thevibratory element 104 commencing at a commanded second frequency and inthe open-loop manner to approximate a second target phase difference ϕ2for the fluid being characterized, vibrate the vibratory element 104 inthe closed-loop manner to achieve the second target phase difference ϕ2and determining a corresponding second frequency point ω2, and determinea viscosity of the fluid being characterized using the first frequencypoint ω1 and the second frequency point ω2.

An open-loop controller, which may also be called a non-feedbackcontroller, computes its input into a system using only a current stateof the system and a model of the system. A characteristic of theopen-loop controller is that it does not use feedback to determine ifthe output has achieved the desired goal of the input. This means thatthe system does not observe the output of the processes that it iscontrolling. Consequently, a true open-loop system cannot correct errorsin the desired and achieved values. It also may not compensate fordisturbances in the system. However, an advanced open-loop system can beused, wherein the control methodology can be self-learning and adaptive.As a result, the vibratory sensor according to any of the embodimentscan employ either a traditional open-loop control process or can employan adaptive open-loop control process, wherein some feedback or outsidevalues are used to ensure that the actual phase difference between thedrive signal phase and the vibration signal phase approximates orclosely approaches the target phase difference.

The drive circuit 138 forces the vibratory element 104 to a vibrationfrequency that is near to the desired vibration frequency by driving itwith an open-loop drive signal to vibrate at the last measured value ofthe frequency point. For instance, by driving a sensor at ω1, with thefrequency obtained from the last measured value of ω1 (referred to as ω1_(time=(t-1))), the drive system is able to approximately locate a newvalue of a first frequency point ω1. Once the commanded first frequencyis achieved, the drive can transition back to a closed-loop operation oran adaptive open-loop operation and locate the exact value of ω1.Similarly, by driving a sensor at ω2, with the frequency obtained fromthe last measured value of ω2 (referred to as ω2 _(time=(t-1))), thedrive system is able to approximately locate a new value of a secondfrequency point ω2. Once the commanded second frequency is achieved, thedrive can transition back to a closed-loop operation or an adaptiveopen-loop operation and locate the exact value of ω2.

As stated above, a purely closed-loop vibration can be used to initiatethe vibration of the vibratory sensor. The vibration can then beswitched to an open-loop vibration, or can be switched to using acombined open-loop and closed-loop vibration, wherein the open-loop partof an iteration greatly shortens an iteration time.

In addition, or alternatively, the meter electronics 20 can decidewhether to employ open-loop vibrations, such as at each iteration, bychecking various environmental factors. For example, the meterelectronics 20 can use the open-loop vibration if the fluid beingcharacterized is acceptably stable. The measured density of the fluidcan be determined to be stable if it does not vary by more than apredetermined density tolerance over a predetermined time period.

FIG. 6 is a flowchart 600 of a method of varying vibration in thevibratory sensor according to an embodiment of the invention. Theclosed-loop method steps 601-604 below determine the frequency of thefirst frequency point ω1 in a closed-loop manner, while the closed-loopmethod steps 605-608 determine the frequency of the second frequencypoint ω2 in a closed-loop manner. The open-loop method steps 620-624below determine the frequency of the first frequency point ω1 in anopen-loop manner, while the open-loop method steps 625-629 determine thefrequency of the second frequency point ω2 in an open-loop manner.

In step 601, a vibration setpoint is set to a first target phasedifference ϕ1 and the vibratory element is vibrated. The target phasedifference is achieved by varying the frequency of the drive signal,starting from the current vibration frequency. The current vibrationfrequency is gradually changed, in a closed-loop manner and according toreceived feedback, such as feedback regarding the difference between acurrent phase difference and the target phase difference. The vibrationfrequency is incrementally ramped up or down from the current vibrationfrequency, depending on whether the phase difference is to be increasedor decreased.

In step 602, the current phase difference is compared to the firsttarget phase difference ϕ1. If the first target phase difference ϕ1 hasbeen achieved, then the method proceeds to step 604. Otherwise, themethod branches to step 603 until the first target phase difference ϕ1is achieved.

In step 603, a wait is performed. Consequently, the method loops andwaits until the vibration setpoint has been achieved. The vibratorysensor therefore waits for the actual vibration of the vibratory elementto reach the vibration setpoint. Due to the closedloop drive operation,the vibratory element does not achieve vibration at the vibrationsetpoint until at least a known wait time has elapsed.

The wait may be for a fixed predetermined time or may vary in length.Environmental conditions may require a longer than expected time toachieve the target phase difference. The length of the wait may dependon various factors. The length of the wait may depend on a distance tothe target phase difference from the initial phase difference. Thelength of the wait may depend on the physical characteristics of thevibratory element. The length of the wait may depend on the nature ofthe fluid being measured (including the density and/or viscosity of thefluid). The length of the wait may depend on the power available to thevibratory sensor. If the available electrical power is limited, thevibratory sensor may not be able to quickly ramp to the target phasedifference and the corresponding frequency point ω1 or ω2.

In step 604, where the vibration setpoint has been achieved and thephase difference between the drive sensor signal and the pickoff sensorsignal corresponds to the first phase difference ϕ1, then thecorresponding first frequency point ω1 is recorded. The first frequencypoint ω1 comprises the vibration frequency that generates the firsttarget phase difference ϕ1. The first frequency point ω1 comprises thefrequency where the phase difference between the drive signal phase andthe pickoff signal phase is about 135 degrees in some embodiments.

In step 605, the vibration setpoint is set to a second target phasedifference ϕ2 and the vibratory element is vibrated from the currentvibration frequency. The second target phase difference ϕ2 is achievedby varying the frequency of the drive signal, starting from the currentvibration frequency. The current vibration frequency is graduallychanged, in a closed-loop manner and according to received feedback,such as feedback regarding the difference between a current phasedifference and the target phase difference. The vibration frequency isincrementally ramped up or down from the current vibration frequency,depending on whether the phase difference is to be increased ordecreased. It should be understood that the starting vibration frequencyis therefore the current vibration frequency, which comprises thevibration frequency obtained in step 604 above.

In step 606, the current phase difference is compared to the secondtarget phase difference ϕ2. If the second target phase difference ϕ2 hasbeen achieved, then the method proceeds to step 608. Otherwise, themethod branches to step 607 until the second target phase difference ϕ2is achieved.

In step 607, a wait is performed. Consequently, the method loops andwaits until the vibration setpoint has been achieved. Due to theclosedloop drive operation, the vibratory element does not achievevibration at the vibration setpoint until at least a known wait time haselapsed, as previously discussed.

In step 608, where the vibration setpoint has been achieved and thephase difference between the drive sensor signal and the pickoff sensorsignal corresponds to the second phase difference ϕ2, then thecorresponding second frequency point ω2 is recorded. The secondfrequency point ω2 comprises the vibration frequency that generates thesecond target phase difference ϕ2. The second frequency point ω2 in someembodiments comprises the frequency where the phase difference betweenthe drive signal phase and the pickoff signal phase is about 45 degreesin some embodiments.

The above closed-loop method steps 601-608 may comprise an initial orstartup iteration for the vibratory flowmeter. The closed-loop methodsteps 601-608 in some embodiments may be used to generate initial valuesof the first and second frequency points ω1 and ω2. The closed-loopmethod steps 601-608 may be iterated one or more times before the methodproceeds to the open-loop method steps 620-629, below.

In step 620, the vibration setpoint is set to the first target phasedifference ϕ1.

In step 621, the vibratory sensor is vibrated at a commanded firstfrequency. Consequently, the vibration of the vibratory sensortransitions discontinuously from a current vibration frequency (i.e.,the vibration frequency as it was immediately before this step) to thefrequency value as given in the commanded first frequency. It shouldtherefore be understood that the initial vibration frequency in thisstep is not the current vibration frequency. Vibration of the vibratorysensor therefore comprises an open-loop vibration process, at least fora period of time. As a result of vibrating in an open-loop manner, theresulting phase difference will immediately be close (or very close) tothe first target phase difference ϕ1 when vibration commences at thecommanded first frequency.

In some embodiments, the commanded first frequency comprises aprevious-time first frequency point ω1 _(time=(t-1)). The subscript[time=(t-1)] signifies that the first frequency point ω1 is from aprevious time period (in the current iteration [time=t]). In someembodiments, the previous-time first frequency point ω1 _(time=(t-1))may comprise the first frequency point ω1 as obtained in a previousiteration of step 604 above, or as obtained in a previous iteration ofstep 624 below. However, it should be understood that the method is notlimited to an immediately previous frequency value, and the value may befrom an iteration farther back in time. Alternatively, the previous-timefirst frequency point ω1 _(time=(t-1)) may comprise an ideal value thatwas previously determined or received and stored within the vibratorysensor, such as an expected frequency value for a predetermined fluid tobe characterized.

It should be understood that after the open-loop vibration transition tothe previous-time first frequency point ω1 _(time=(t-1)), the vibrationmay then return to a closed-loop or adaptive open-loop vibrationprocess. Feedback (or other or additional information) may then beemployed to refine the vibration and zero in on the first target phasedifference ϕ1.

In step 622, the current phase difference is compared to the firsttarget phase difference ϕ1. If the first target phase difference ϕ1 hasbeen achieved, then the method proceeds to step 624. Otherwise, themethod branches to step 623 until the first target phase difference ϕ1is achieved. In step 623, a wait is performed. Consequently, the methodloops and waits until the vibration setpoint has been achieved. The waitmay be for a fixed predetermined time or may vary in length. The lengthof the wait may depend on various factors, such as the distance to thetarget phase difference from the initial phase difference, the physicalcharacteristics of the vibratory element, the nature of the fluid beingmeasured (including the density and/or viscosity of the fluid), and thepower available to the vibratory sensor. However, the wait of step 623will be significantly less than the wait length of step 603 above.Because step 621 vibrates the vibratory sensor in an open-loop manner,and starts with a frequency that will be close to the final frequency,the amount of time needed for the vibratory sensor to achieve the targetphase difference is significantly reduced.

In step 624, where the vibration setpoint has been achieved and thephase difference between the drive sensor signal and the pickoff sensorsignal corresponds to the first phase difference ϕ1, then thecorresponding first frequency point ω1 is recorded. The first frequencypoint ω1 comprises the vibration frequency that generates the firsttarget phase difference ϕ1. The first frequency point ω1 comprises thefrequency where the phase difference between the drive signal phase andthe pickoff signal phase is about 135 degrees in some embodiments.

The newly-determined first frequency point ω1 in some embodiments may beused as the previous-time first frequency point ω1 _(time=(t-1)) in afuture iteration (or iterations) of the open-loop method steps 620-624.

In step 625, the vibration setpoint is set to the second target phasedifference ϕ2.

In step 626, the vibratory sensor is vibrated at a commanded secondfrequency. Consequently, the vibration of the vibratory sensortransitions discontinuously from a current vibration frequency (i.e.,the vibration frequency as it was immediately before this step) to thefrequency value as given in the commanded second frequency. It shouldtherefore be understood that the initial vibration frequency in thisstep is not the current vibration frequency. Vibration of the vibratorysensor therefore comprises an open-loop vibration process, at least fora period of time. As a result of vibrating in an open-loop manner, theresulting phase difference will immediately be close (or very close) tothe second target phase difference ϕ2 when vibration commences at thecommanded second frequency.

In some embodiments, the commanded second frequency comprises aprevious-time second frequency point ω2 _(time=(t-1)). The subscript[time=(t-1)] signifies that the second frequency point ω2 is from aprevious time period (in the current iteration [time=t]). In someembodiments, the previous-time second frequency point ω2 _(time=(t-1))may comprise the second frequency point ω2 as obtained in a previousiteration of step 608 above, or as obtained in a previous iteration ofstep 629 below. However, it should be understood that the method is notlimited to an immediately previous frequency value, and the value may befrom an iteration farther back in time. Alternatively, the previous-timesecond frequency point ω2 _((time=(t-1)) may comprise an ideal valuethat was previously determined or received and stored within thevibratory sensor, such as an expected frequency value for apredetermined fluid to be characterized.

It should be understood that after the open-loop vibration transition tothe previous-time second frequency point ω2 _(time=(t-1)), the vibrationmay then return to a closed-loop or adaptive open-loop vibrationprocess. Feedback (or other or additional information) may then beemployed to refine the vibration and zero in on the second target phasedifference ϕ2.

In step 627, the current phase difference is compared to the secondtarget phase difference ϕ2. If the second target phase difference ϕ2 hasbeen achieved, then the method proceeds to step 629. Otherwise, themethod branches to step 628 until the second target phase difference ϕ2is achieved.

In step 628, a wait is performed. Consequently, the method loops andwaits until the vibration setpoint has been achieved. The wait may befor a fixed predetermined time or may vary in length. The length of thewait may depend on various factors, such as the distance to the targetphase difference from the initial phase difference, the physicalcharacteristics of the vibratory element, the nature of the fluid beingmeasured (including the density and/or viscosity of the fluid), and thepower available to the vibratory sensor. However, the wait of step 628will be significantly less than the wait length of step 607 above.Because step 626 vibrates the vibratory sensor in an open-loop manner,and starts with a frequency that will be close to the final frequency,the amount of time needed for the vibratory sensor to achieve the targetphase difference is significantly reduced.

In step 629, where the vibration setpoint has been achieved and thephase difference between the drive sensor signal and the pickoff sensorsignal corresponds to the second phase difference ϕ2, then thecorresponding second frequency point ω2 is recorded. The secondvibration frequency point ω2 comprises the vibration frequency thatgenerates the second target phase difference ϕ2. The second frequencypoint ω2 comprises the frequency where the phase difference between thedrive signal phase and the pickoff signal phase is about 45 degrees insome embodiments.

The newly-determined second frequency point ω2 in some embodiments maybe used as the previous-time second frequency point ω2 _(time=(t-1)) ina future iteration (or iterations) of the open-loop method steps625-629.

The vibratory sensor 5 according to any of the embodiments reacts fasterchanges in the fluid being characterized using the open-loop operation.

It should be understood that the closed-loop method steps 601-608 maycomprise an initial or startup process, wherein the closed-loop methodsteps 601-608 are executed at least once. The closed-loop method steps601-608 may be not executed during normal operation or after the initialor startup process. In some embodiments, the open-loop method steps620-629 may be iteratively executed and the closed-loop method steps601-608 are executed merely to derive initial values of the frequencypoints ω1 and ω2. Alternatively, in some embodiments the stepsclosed-loop method 601-608 may be executed periodically orintermittently, including on an as-needed basis, for example.

In an alternative embodiment, the first and second frequency points ω1and ω2 may be found by measuring the power of the vibration signal anddetermining the first and second frequency points ω1 and ω2 from thepoints of half-power in the vibration signal. It should be understoodthat the frequency points found by measuring power may be approximatelythe same as the frequency points found by monitoring the phasedifference, but may not be exactly the same.

FIG. 7 is a graph of the combined closed-loop and open-loop vibrationresponses of the vibratory sensor of FIGS. 4-5 and/or the combinedclosed-loop and open-loop vibration responses of the method of FIG. 6.The vertical axis represents vibration frequency (ω) and the horizontalaxis represents time (t). It can be seen that the prior art vibratorysensor is alternatingly vibrated at the first frequency point ω1 andthen at the second frequency point ω2, wherein this pattern isiteratively repeated. Although the frequency points ω1 and ω2 are shownas being constant, it should be understood that the first and secondfrequency points ω1 and ω2 may change due to changes in the fluid beingcharacterized by the vibratory sensor, for example. In addition, thefirst and second frequency points ω1 and ω2 may change due to changes inenvironmental conditions, such as due to changes in temperature and/orpressure, for example.

The first two vibration occurrences span two closed-loop time periodsT_(CL). The first two vibration occurrences comprise vibration in aclosed-loop manner, wherein vibration commences at the frequency pointω1 and the vibration is smoothly and continuously varied until thevibration achieves the frequency point ω2 or the vibration commences atthe frequency point ω2 and the vibration is smoothly and continuouslyvaried until the vibration achieves the frequency point ω1. Due to theclosed-loop vibration in the first two vibration occurrences, it can beseen that the actual vibration frequency changes smoothly andcontinuously, but slowly. Each change in drive frequency requires aclosed-loop time period T_(CL) to accomplish, due to the feedback usedto achieve the target phase difference. As a result, the prior artvibratory tine sensor cannot measure rapid changes in the frequencypoints ω1 and ω2, and therefore cannot measure rapid changes in densityand/or viscosity of the fluid to be characterized.

The subsequent seven vibration occurrences shown in the figure spanopen-loop time periods T_(OL). The subsequent seven vibrationoccurrences comprise vibration in an open-loop manner, wherein vibrationcommences at a commanded target vibration and the vibrationdiscontinuously transitions from a previous vibration to the commandedtarget vibration. For example, at the beginning of the first open-looptime period T_(OL) (point A on the graph), where the vibration frequencyis currently the second frequency point ω2, the vibration neverthelesstransitions abruptly and discontinuously to the first frequency point ω1(point B).

As stated above, a purely closed-loop vibration can be used to initiatevibration. The vibration can then switch to using a purely open-loopvibration, or can switch to using a combined open-loop and closed-loopvibration, wherein the open-loop part of an iteration greatly shortensan iteration time.

In addition, or alternatively, the meter electronics 20 can decidewhether to employ open-loop vibration, such as at each iteration, bychecking various environmental factors. For example, the meterelectronics 20 can use the open-loop vibration if the fluid beingcharacterized is substantially stable. The measured density of the fluidcan be determined to be stable if it does not vary by more than apredetermined density tolerance over a predetermined time period.

The detailed descriptions of the above embodiments are not exhaustivedescriptions of all embodiments contemplated by the inventors to bewithin the scope of the invention. Indeed, persons skilled in the artwill recognize that certain elements of the above-described embodimentsmay variously be combined or eliminated to create further embodiments,and such further embodiments fall within the scope and teachings of theinvention. It will also be apparent to those of ordinary skill in theart that the above-described embodiments may be combined in whole or inpart to create additional embodiments within the scope and teachings ofthe invention. Accordingly, the scope of the invention should bedetermined from the following claims.

What is claimed is:
 1. A vibratory sensor (5), comprising: a vibratoryelement (104) configured to generate a vibration signal; and a receivercircuit (134) that receives the vibration signal from the vibratoryelement (104); and a drive circuit (138) coupled to the receiver circuit(134) and the vibratory element (104) and generating a drive signal thatvibrates the vibratory element (104), wherein the drive circuit (138)vibrates the vibratory element (104) commencing at a commanded firstfrequency and in an open-loop manner to achieve a first target phasedifference ϕ1 for a fluid being characterized and determines acorresponding first frequency point ω1, vibrates the vibratory element(104) commencing at a commanded second frequency and in the open-loopmanner to achieve a second target phase difference ϕ2 and determines acorresponding second frequency point ω2, and determines a viscosity ofthe fluid being characterized using the first frequency point ω1 and thesecond frequency point ω2.
 2. The vibratory sensor (5) of claim 1, withthe vibratory sensor (5) iteratively performing the vibrating anddetermining steps.
 3. The vibratory sensor (5) of claim 1, with thecommanded first frequency comprising a previous-time first frequencypoint ω1 _(time=(t-1)) and with the commanded second frequencycomprising a previous-time second frequency point ω2 _(time=(t-1)). 4.The vibratory sensor (5) of claim 1, with the drive circuit (138)comprising a closed-loop drive (143) that generates the drive signal toachieve a target phase difference and commencing at a current vibrationfrequency and an open-loop drive (147) that generates the drive signalto achieve a target phase difference and commencing at a commanded firstor second frequency.
 5. The vibratory sensor (5) of claim 1, withvibrating the vibratory element (104) of the vibratory sensor in theopen-loop manner comprising: the drive circuit (138) setting a vibrationsetpoint to the first target phase difference ϕ1; the drive circuit(138) vibrating the vibratory element (104) in the open-loop manner andat the commanded first frequency; the drive circuit (138) comparing acurrent first phase difference to the first target phase difference ϕ1and waiting until the current first phase difference is substantiallyequal to the first target phase difference ϕ1; if the current firstphase difference is equal to the first target phase difference ϕ1, thenthe drive circuit (138) recording the corresponding first frequencypoint ω1, wherein achieving the first target phase difference ϕ1generates the first frequency point ω1 in the vibratory element (104);the drive circuit (138) setting the vibration setpoint to the secondtarget phase difference ϕ2; the drive circuit (138) vibrating thevibratory element (104) in the open-loop manner and at the commandedsecond frequency; the drive circuit (138) comparing a current secondphase difference to the second target phase difference ϕ2 and waitinguntil the current second phase difference is substantially equal to thesecond target phase difference ϕ2; and if the current second phasedifference is equal to the second target phase difference ϕ2, then thedrive circuit (138) recording the corresponding second frequency pointω2, wherein achieving the second target phase difference ϕ2 generatesthe second frequency point ω2 in the vibratory element (104).
 6. Thevibratory sensor (5) of claim 1, with the drive circuit (138) beingfurther configured to: vibrate the vibratory element (104) in aclosed-loop manner to achieve the first target phase difference ϕ1 forthe fluid being characterized and determining a corresponding firstfrequency point ω1, with the vibrating commencing at the currentvibration frequency; and vibrate the vibratory element (104) in theclosed-loop manner to achieve the second target phase difference ϕ2 forthe fluid being characterized and determining a corresponding secondfrequency point ω2, with the vibrating commencing at the currentvibration frequency.
 7. The vibratory sensor (5) of claim 1, wherein thedrive circuit (138) selects the open-loop operation if the fluid beingcharacterized is substantially stable.
 8. The vibratory sensor (5) ofclaim 1, with the drive circuit (138) being further configured to:vibrate the vibratory element (104) commencing at the commanded firstfrequency and in the open-loop manner to approximate the first targetphase difference ϕ1 for a fluid being characterized; vibrate thevibratory element (104) in a closed-loop manner to achieve the firsttarget phase difference ϕ1 and determine a corresponding first frequencypoint ω1; vibrate the vibratory element (104) commencing at thecommanded second frequency and in the open-loop manner to approximatethe second target phase difference ϕ2 for the fluid being characterized;vibrate the vibratory element (104) in the closed-loop manner to achievethe second target phase difference ϕ2 and determine a correspondingsecond frequency point ω2; and determine a viscosity of the fluid beingcharacterized using the first frequency point ω1 and the secondfrequency point ω2.
 9. The vibratory sensor (5) of claim 1, with thereceiver circuit (134) being coupled to the drive circuit (138), withthe receiver circuit (134) providing the vibration signal amplitude andthe vibration signal frequency to the drive circuit (138), with thedrive circuit (138) generating a drive signal for the vibratory element(104) using the vibration signal amplitude and the vibration signalfrequency.
 10. The vibratory sensor (5) of claim 1, with the vibratorysensor (5) comprising a vibratory tine sensor (5) and with the vibratoryelement (104) comprising a tuning fork structure (104).